State estimation of probabilistic hybrid systems with particle filters

Robotic and embedded systems have become increasingly pervasive in every-day applications, ranging from space probes and life support systems to autonomous rovers. In order to act robustly in the physical world, robotic systems must handle the uncertainty and partial observability inherent in most real-world situations. A convenient modeling tool for many applications, including fault diagnosis and visual tracking, are probabilistic hybrid models. In probabilistic hybrid models, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. The hidden state is observed indirectly, through noisy observations. A challenge is that real-world systems are non-linear, consist of a large collection of concurrently operating components, and exhibit autonomous mode transitions, that is, discrete state transitions that depend on the continuous dynamics. In this thesis, we introduce an efficient algorithm for hybrid state estimation that combines Rao-Blackwellised particle filtering with a Gaussian representation. Conceptually, our algorithm samples trajectories traced by the discrete variables over time and, for each trajectory, estimates the continuous state with a Kalman Filter. A key insight to handling the autonomous transitions is to reuse the continuous estimates in the importance sampling step. We extended the class of autonomous transitions that can be efficiently handled by Gaussian techniques and provide a detailed empirical evaluation of the algorithm on a dynamical system with four continuous state variables. Our results indicate that our algorithm is substantially more efficient than non-RaoBlackwellised approaches. Though not as good as a k-best filter in nominal scenarios, our algorithm outperforms a k-best filter when the correct diagnosis has too low a probability to be included in the leading set of trajectories. Through these accomplishments, the thesis lays ground work for a unifying stochastic search algorithm that shares the benefits of both methods. Thesis Supervisor: Brian C. Williams Title: Associate Professor